Download Invited Paper Theory and Measurement Techniques for the Noise

Optical Fiber Technology 6, 122᎐154 Ž2000.
doi:10.1006rofte.2000.0327, available online at http:rrwww.idealibrary.com on
Invited Paper
Theory and Measurement Techniques for the
Noise Figure of Optical Amplifiers
Douglas M. Baney
Agilent Laboratories, 3500 Deer Creek Road, Palo Alto, California 94304
Philippe Gallion
Ecole Nationale Superieure des Telecommunications, 46 rue Barrault,
Paris Cedex 13, France
and
Rodney S. Tucker
Australian Photonics Cooperati¨ e Research Centre, Department of Electrical and Electronic
Engineering, Uni¨ ersity of Melbourne, Park¨ ille, Victoria 3052, Australia
Received December 29, 1999
The theoretical basis for the noise figure of optical amplifiers is reviewed,
and a consistent approach to determining the noise figure of cascaded
components is developed. It is shown that when the noise figure is defined in
terms of the input and output signal-to-noise ratios, the formulation provides
a consistent theoretical formulation for measurement techniques using optical and optoelectronic measurement methods. The paper concludes with a
review of measurement techniques for characterization of the noise figure.
䊚 2000 Academic Press
I. INTRODUCTION
Optical amplifiers are used extensively in optical fiber telecommunications. By
injecting laser pump light at a wavelength of 980 or 1480 nm into a strand of
erbium-doped optical fiber, high optical gain at wavelengths between 1.5 and 1.6
␮ m can be obtained w1x. Erbium-doped fiber amplifiers ŽEDFAs. routinely amplify
dozens of wavelengths simultaneously to compensate for signal power losses due to
122
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Copyright 䊚 2000 by Academic Press
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NOISE FIGURE OF OPTICAL AMPLIFIERS
123
splitting and propagation through optical fiber. In addition to providing optical
gain, amplifiers also add undesired optical power fluctuations onto the signal. This
intensity noise can lead to poor signal reception in analog communications or high
bit-error rates in digital transmission systems w2x. In electronic amplifiers, it is
common to quantify the effects of noise using a parameter known as the noise
figure. This concept of a noise figure can also be applied to optical amplifiers w1᎐5x,
but it should be noted that not all definitions in the literature are the same. The
purpose of the present paper is to present a consistent approach to modeling the
noise figure of optical amplifiers and other optical components and to review noise
figure measurement techniques.
The undesired optical power fluctuations Žintensity noise. introduced by optical
components cause transmission impairments in optical communications systems.
This noise can be characterized indirectly by measuring the optical field power
spectrum and using an approximate model to evaluate the intensity noise. Alternatively, optoelectronic detection is used where a photodetector converts the optical
power into an electrical signal and the accompanying noise is analyzed using
standard electronic techniques. Characterization of the noise figure of an optical
amplifier can be straightforward or complicated depending on the context in which
the noise figure data are employed. For the simple situation where the noise figure
is used to quantify the contribution of the EDFA to the accumulation of amplified
spontaneous emission ŽASE. in a cascade of amplifiers, optical measurement
methods are commonly used. In cases where the complete noise figure is required,
such as when optical reflection-induced intensity noise must be considered, optoelectronic measurement methods should be used. The model presented here
applies to both optical and optoelectronic noise figure measurement techniques.
Reduced to its simplest form, it is shown to be consistent with the noise figure as
defined by the IEC ŽSC86C, Working Group 3., the international standards body
responsible for optical amplifier noise figure definitions. That definition has been
adopted by the ITU-T ŽInternational Telecommunications UnionᎏTelecommunications. and is in use by the major test instrument and optical amplifier equipment
manufacturers w6x.
The paper is structured as follows. We begin with a discussion of noise figure in
optical amplifiers and other optical components. In Section II we present a model
of noise in optical two-port devices. Section III defines the optical noise figure,
which is then cast in terms of measurable parameters in Section IV. The expected
ASE at the end of an amplifier cascade is derived in Section V. Section VI reviews
various optical and optoelectronic techniques for noise figure measurement.
II. INTENSITY NOISE
The principle sources of transmission impairment in intensity-modulated communications systems are timing jitter and intensity noise w2, 5x. EDFAs can
contribute significantly to intensity noise degradation resulting in vertical closure
of the eye pattern of detected intensity-keyed signals as viewed on an oscilloscope.
The effect of intensity noise is illustrated in Fig. 1. The transmitter output shown in
124
BANEY, GALLION, AND TUCKER
FIG. 1. Signal degradation due to amplifier produced noise: Ža. Transmitter output with SNR as
limited by laser RIN. Žb. Received signal corrupted by beat, multipath interference and shot noise.
Fig. 1a has a good signal-to-noise ratio ŽSNR. which is limited by the excess
relative intensity noise ŽRIN. or shot noise of the transmitter laser. After traversing
an optical network composed of transmission fiber and optical amplifiers, the SNR
becomes degraded, as shown in Fig. 1b. This increases the errors generated by
decision circuits that determine whether a logical ‘‘1’’ or ‘‘0’’ was transmitted.
Contributions to intensity noise include w1᎐3, 5᎐12x:
䢇
Signal-spontaneous Žsig-sp. beating
䢇
Spontaneous-spontaneous Žsp-sp. beating
䢇
Multipath interference ŽMPI.
䢇
Amplified double-Rayleigh backscatter
䢇
Shot noise due to signal, ASE, and the remnant pump light.
Figure 1b indicates which of these contribution affect the logical ‘‘1’’ and ‘‘0’’
levels.
Figure 2 shows the distributions of some of the intensity noise sources inherent
to the optical amplifier. Figure 2a shows the distributions of the optical field
spectrums S E Ž ␯ . and the associated signal-spontaneous beating, which originates
from the mixing or beating of the coherent signal with the incoherent ASE in the
same polarization. The curve on the left of Fig. 2a is the optical field power
spectrum Žmeasurable with an optical spectrum analyzer. and the curve on the
right is the intensity spectrum Žmeasurable using a photodetector and an electrical
spectrum analyzer.. Note that ␯ is the frequency of the optical field and f is the
baseband frequency of the electrical output from the photodetector. For reference,
very approximate values of optical frequency and baseband frequency are given in
NOISE FIGURE OF OPTICAL AMPLIFIERS
125
FIG. 2. Distributions of some of the intensity noise sources created by the optical amplifier. SE Ž ␯ .
optical field power spectrum, SP Ž f . intensity spectrum.
Fig. 2. Note that the bandwidth of the intensity spectrum shown here is limited to
about 50 GHz by optical filtering after the amplifier. ŽThe optical bandwidth is Bo ..
Figure 2b shows the optical field power spectrum and the intensity spectrum of
sp-sp beat noise w1᎐3, 5, 7x. Beating of copolarized spectral components of ASE
causes sp-sp beat noise. This noise is also dependent on the baseband frequency,
with the noise density decreasing with increasing baseband frequency, f. In
principle, the spontaneous᎐spontaneous intensity spectrum could be as wide as the
optical amplifier bandwidth Ž) 5000 GHz. in the absence of optical filtering, but
this would generally not be measurable due to the limited bandwidth of practical
photodetectors and electrical spectrum analyzers.
Figure 2c illustrates another important intensity noise known as MPI noise. MPI
noise arises from the conversion of phase or frequency noise associated with the
signal to intensity noise. This occurs within optical amplifiers. Figure 3 shows the
structure of a typical EDFA. The various components Že.g., isolators, multiplexers,
erbium-doped fiber. that constitute the optical amplifier contribute optical reflections in the signal path. These reflections are highlighted in Fig. 3. In a manner
similar to a frequency discriminator, these reflections convert signal phase and
frequency fluctuations into intensity noise. Optical reflections may also enhance
ASE production by the amplifier. The expected intensity noise is shown in Fig. 2c
for two reflections situated on either side of internal gain, Gi nt . G gives the
amplifier net gain, and the laser linewidth ŽLorentzian. ⌬ ␯ is such that the time
126
BANEY, GALLION, AND TUCKER
FIG. 3. A simple erbium-doped fiber optic amplifier showing its basic components. Components
have optical reflections R and attenuation ␣ k that contribute to the noise generated by the amplifier.
ISO, optical isolator; EDF, erbium doped fiber; GEQ, gain equalizer; ASE, amplified spontaneous
emission.
delay between the reflections exceeds the coherence time of the laser w3x. In
practice, the time delay may not always exceed the coherence time and multiple
reflections of unknown strengths and polarizations can interfere. MPI noise is
baseband frequency-dependent and is of particular importance when optical amplifiers are used for CATV, sensing, and high-frequency subcarrier transmission w12x.
Another important effect is simulated Brillouin backscatter ŽSBS., which is due to
acoustic waves in optical fiber caused by a strong optical signal field. SBS is known
to cause significant baseband frequency noise with a peak around 11 GHz w3x. Even
the intrinsic molecular level variations of the index of refraction of glass causes
reflections, known as Rayleigh backscatter, that can contribute significant noise in
high gain amplifiers w10, 11x.
The noise sources described above can be categorized into a noise grouping
known as excess noise. This is illustrated in Fig. 4, which shows schematically how
the noise level can lie anywhere between zero and infinity, depending on the noise
source and the optical attenuation. In the squeezed regime w13, 14x, the noise level
of an optical signal at a given power level is less than the shot noise that would
normally be associated with a signal at that power level. The noise level of a
squeezed signal typically increases Žrelative to the signal level. in the presence of
optical attenuation. As the attenuation increases, the noise level approaches the
FIG. 4. Regimes of noise level relative to signal power. In the presence of optical attenuation, all
noise converges to shot noise.
NOISE FIGURE OF OPTICAL AMPLIFIERS
127
usual shot noise level associated with a signal of that power level. Of greater
practical significance than the squeezed noise regime is the excess noise regime. In
this regime, the noise level is higher than the level of shot noise, due to the
influence of excess noise sources such as signal᎐spontaneous beat noise, etc. In the
excess noise regime, the noise decreases with increasing attenuation and converges
to pure shot noise.
Given the number of different noise sources, and the fact that the importance of
the individual noise sources varies with the application and design of the amplifier,
a correct definition of noise figure should include all contributions to noise. The
noise figure formulation provided in this paper is based on a general description of
the SNR degradation of intensity modulated signals used in direct detection optical
systems that are currently in widespread use. The approach presented here is valid
for all types of intensity noise.
III. NOISE FIGUREᎏDEFINITION
Signal-to-Noise Ratio
Prior to defining the noise figure, we will define the SNR, which forms the basis
of optical amplifier and optical component noise figure calculations. The SNR
serves as a measure of the quality of a signal. It is determined in terms of the signal
and noise levels in the photocurrent of a photodetector placed in the signal path.
The SNR can be calculated in terms of the received signal photocurrent, i sig , and
the variance of the received photocurrent noise ² ⌬2 i n :.
SNR s
² i sig :2
² ⌬2 i n :
,
Ž 1.
where the noise variance ² ⌬2 i n : is found by integrating the received intensity noise
spectrum over the bandwidth of interest w3x.
² ⌬2 i n : s ᑬ 2
HB S
P
Ž f . df ,
Ž 2.
e
where SP Ž f . is the power spectral density of the undesired power fluctuations
accompanying the signal, Be is the photodetector bandwidth, ᑬ is the photodetector responsivity with units of ampsrwatt, and f is the electrical baseband frequency. Note that the SNR is defined in terms of a ratio of power levels of the
photocurrent. Thus the SNR is a ratio of electrical power levels rather than a ratio
of optical power levels.
Noise Figure
Just as the SNR serves as a figure of merit to characterize the noise quality of a
signal, the noise generation nature of optical amplifiers or other components can
be characterized by the noise figure of the component. The noise figure enables
128
BANEY, GALLION, AND TUCKER
system and component designers to evaluate the impact of a component on the
SNR of a signal passing through that component. Noise figure quantifies the
degradation of the SNR due to the insertion of an amplifier or component in a
signal transmission. Noise figure thus reflects the impact of the diversity of noise
sources that impact the overall noise performance of the amplifier or component.
We begin by defining the noise factor. Using the nomenclature of the IEC, wIEC
61291-1x, the noise factor F is defined by
FŽ␯ , f . s
SNR in
SNR out Ž ␯ , f .
,
Ž 3.
where SNR in is the SNR at the amplifier input and SNR out is the SNR at the
output. In general, noise factor is a function of both the optical frequency ␯ and
the baseband frequency f w3, 8, 12x. In order to provide consistency and repeatability, it is necessary that SNR in is fixed and known. We return to this important issue
below, where we discuss the choice of the input noise reference signal used in the
measurements.
The noise figure ŽNF. is the noise factor expressed in decibel units:
NF s 10 log 10 Ž F . .
Ž 4.
This notation is used through this article to be consistent with IEC usage. The
noise factor in Eq. w4x is consistent with the definition of SNR as a ratio of detected
photoelectric power levels. Thus the NF is expressed correctly in electrical dB
rather than in optical dB.
The general concept of noise figure measurement is illustrated in Fig. 5.
Essentially, noise figure describes the SNR degradation when the component is
inserted at specified measurement reference planes and boundary conditions. In
FIG. 5. Noise figure is defined as the ratio of input to output SNRs for an ideal receiver when
illuminated by a shot-noise-limited source. Ža. Measurement of input SNR, SNR in ; Žb. Measurement of
output SNR, SNR out showing sources of noise from optical amplifier.
NOISE FIGURE OF OPTICAL AMPLIFIERS
129
practice, this can be achieved using a receiver that measures the input SNR,
SNR in , and the output SNR, SNR out , using a substitution method. To be useful, it
is important that measurements of noise figure are independent of the nonidealities of the system used in its characterization. This point is quite important since it
greatly affects the methods used to characterize the amplifier. If noise figure
measurements could not be separated from the characteristics of individual test
setups, then it would be difficult to compare results between different testing
laboratories. For this reason the test setup must use ideal sources and receivers; if
not, a correction for the source and receiver nonidealities is required. We will
return to this in Section VI, where we review NF measurement techniques.
Input Noise Reference Signal
We now look at the choice of an input reference signal for use in noise figure
measurements and calculations. Okoshi and Kikuchi w2x defined noise figure in
terms of a coherent input reference signal without any excess noise. In other
words, their definition uses a shot-noise-limited input reference. The shot-noiselimited input reference is widely used in the literature w1᎐3, 5, 6, 12, 15᎐21x, it has
been implemented by the noise figure instrument makers w20x, and it is incorporated into the international definition of noise figure by the IEC wIEC 61291-1x.
Since shot noise arises from the particulate nature of uncorrelated photons or
electrons. It represents the minimum practical noise Žballistic transport regime.
obtainable in photonic or electronic circuits. An additional feature of the shot
noise reference is that any signal will become shot-noise limited with sufficient
attenuation. This feature has proven very useful in amplifier testing when only
lasers with excess noise Žbeyond shot noise. are available for measurement w3x.
In principle, it would be possible to use squeezed light as an input noise
reference signal. As pointed out earlier, it is possible to obtain a noise level below
shot noise through squeezing w13, 14x. This is the so-called nonclassical intensitysqueezed light. The degree of squeezing is rapidly lost if any loss Žor gain. is
present in the propagation path. Due to the delicate nature of squeezed light with
respect to absorption, we believe that it does not provide a convenient measurable
input noise reference.
A third alternative for the input noise reference is to use a signal with a known
amount of excess noise. This approach is analogous to the noise figure definition
used in electrical circuits, where the input reference signal is based on thermal
noise at a room temperature of 290 K. A significant disadvantage of using excess
noise as a reference in noise figure measurements on low-noise optical components
such as amplifiers is that the excess noise at the input can mask the noise produced
by the amplifier under test. A consequence of this is a reduction in the accuracy of
noise figure measurements that use excess noise at the input.
IV. NOISE FIGURE IN TERMS OF MEASURABLE PARAMETERS
In this section we explore the detailed noise figure characteristics of optical
amplifiers and other optical components. We begin with the input and output SNR.
130
BANEY, GALLION, AND TUCKER
Input SNR
As discussed above, the input signal is defined to be shot-noise-limited. Its
signal-to-noise ratio SNR in is measured as shown in Fig. 5, and the measured SNR
for a shot-noise-limited source is given by w1᎐3x
SNR in s
² i in :2
²⌬ in:
2
s
ᑬ 2 Pin2
2 qᑬ Pin Be
s
␩ Pin
2 h ␯ Be
,
Ž 5.
where i in is the photocurrent generated by the optical signal of power level Pin .
The photodetector responsivity is ᑬ s ␩ qrh␯ where ␩ is the photodetector
quantum efficiency and Be is the baseband bandwidth of the noise. The term ² i in :2
in the numerator of Eq. Ž5. is proportional to the detected electrical signal power
and the ² ⌬2 i n : term in the denominator is the mean-square value of a single-sided
noise power spectrum. Equation Ž5. shows that the detected signal power depends
on the square of Pin and that the shot noise is proportional to Pin . Note that SNR in
depends on the quantum efficiency of the receiver. The noise factor defined below
assumes an ideal receiver, which means that it is usually necessary to calibrate the
receiver and numerically correct for the nonunity quantum efficiency. For an ideal
receiver with negligible thermal noise, and a noise bandwidth Be of 1 Hz, Eq. Ž5.
becomes
SNR in s
Pin
2 h␯
.
Ž 6.
An alternative approach to deriving Eq. Ž5. is by adding the so-called zero point
fluctuations, N, with a single-sided spectral density of h␯r2, to a classical signal
A o normalized such that < A o < 2 is the optical power Pin . The resulting instantaneous
optical power fluctuations are <Ž A o q N .< 2 f Pin q 2 ANi where Ni is the in-phase
component of N. Note that the bandwidth associated with N is twice the baseband
bandwidth for the in-phase and the quadrature components and these two components equally share the total noise power for the coherent Žnonsqueezed. light
ascribed to the shot-noise-limited signal. The power fluctuation ⌬ Pin s 2 ANi has
an associated power spectrum of 2 h␯ that is four times the zero-point fluctuations.
Output SNR
The output noise depends on a number of contributing noise sources, with
differing spectral densities and with differing significance depending on the context
within which the amplifier is used. Since the output signal-to-noise ratio is based
on measurable optical power levels and not optical field quantities, it can be
measured in an identical way to the Žreciprocal. RIN used to describe laser noise
w2, 3, 17x. The output SNR is often normalized to a 1 Hz bandwidth as with the
input SNR, which also makes it consistent with the common usage of RIN.
The output signal-to-noise ratio is given by
SNR out s
² i out :2
² ⌬2 i out :
,
Ž 7.
131
NOISE FIGURE OF OPTICAL AMPLIFIERS
where
² i out :2 s ᑬ 2 G 2 Pin2 .
The most direct approach to determine the denominator of Eq. Ž7. is to simply add
the intensity noise power spectral densities of all the contributing uncorrelated
noise sources. The measured output SNR then becomes
SNR out s
ᑬ 2 G 2 Pin2
Be ᑬ 2 Ssig-sp q Ssp-sp q S MPI q Spump q ⭈⭈⭈ q␩y1 Sshot .
,
Ž 8.
where G is the optical gain of the amplifier and Ssig-sp , Ssp-sp , S MPI , Spump , and Sshot
are the baseband noise spectral densities of signal-spontaneous beat noise, spontaneous᎐spontaneous beat noise, multipath interference noise, pump noise, and shot
noise, respectively. Note that the responsivity of the photodetector appears in the
numerator and denominator. Therefore, its value does not need to be known in
order to measure the output SNR. However, the photodetector quantum efficiency
␩ appears in the shot noise term in the denominator because the number of
detected photoelectrons differs from the number of photons that impinge on the
photodetector. The noise figure is defined in terms of an ideal receiver, in which
the quantum efficiency is unity. Thus when calculating the noise factor, it may be
necessary to correct the measured SNR out to account for nonunity quantum
efficiency.
In general, the denominator of Eq. Ž8. depends on the optical frequency ␯ and
the baseband frequency f. Rather than attempting to detail all of the individual
frequency-dependent contributions to the denominator, we lump the noise terms in
the denominator into the two noise categories: excess noise and shot noise w22x.
Thus, the measured output SNR becomes
SNR out s
G 2 Pin2
Be S e Ž ␯ , f . q ␩y1 Sshot
,
Ž 9.
where the spectral density S e Ž ␯ , f . includes all excess noise contributions to the
output noise.
To obtain the amplifier noise factor as defined by Eq. Ž3., it is necessary to
correct for source and receiver nonidealities, such as nonunity receiver quantum
efficiency. When these nonidealities are corrected, the noise factor, according to
Eqs. Ž3., Ž5., and Ž9., is:
FŽ␯ , f . s
Se Ž ␯ , f .
2 h␯ G Pin
2
q
Sshot
2 h␯ G 2 Pin
Ž 10 .
F s Fexcess q Fshot
S e Ž ␯ , f . Žunits: W 2rHz. is the overall amplifier-generated excess intensity noise
density, h␯ Žunits: joules. is the photon energy, G is the gain, and Pin Žunits: W. is
the incident signal power w22x. The noise figure dependence on optical frequency,
132
BANEY, GALLION, AND TUCKER
␯ , and baseband frequency, f, arises through the dependence of S e on these
variables. Equation Ž10. provides a basis for the measurement of F. The spectral
density S e is measured using electrical techniques at baseband frequencies, and if
the other parameters are known or measured by standard optical measurements,
the noise factor can be determined. This measurement method is referred to below
as the optoelectronic or electrical method.
Next it will be shown that the standard optical noise factor used in the fiberoptic
communications industry is a special case of Eq. Ž10. where all sources of SNR
degradation are usually ignored except for signal-spontaneous beat and shot noise
due to the received signal. This represents the best noise performance that a high
gain amplifier can achieve when the input channel power is above the effective
input noise of the amplifier for a given optical receiver bandwidth. For a typical
100 GHz ITU channel spacing with 10 GBrs transmission rates, the effective input
noise Ž;2 h␯ Be . is y50 dBm. This is well below the minimum channel powers
used in these links.
As shown in Fig. 2, the well-known signal-spontaneous beat noise density
depends on the product of the ASE density in the same polarization state as the
signal and the amplified optical signal w3, 7x. At baseband frequencies below about
50 GHz the signal-spontaneous beat noise density is
Ssig-sp s 4 ␳ASE GPin .
Ž 11 .
The shot-noise density due to the detected signal power Pin is
Sshot s 2 h␯ GPin .
Ž 12 .
Putting S e s Ssig-sp in Eq. Ž10., and substituting Eqs. Ž12. and Ž11., we obtain:
F s Fsig-sp q Fshot ,
Ž 13 .
where
Fsig-sp s
2 ␳ASE
Gh␯
and
Fshot s
1
G
.
Equation Ž13. gives the noise factor for situations where signal-spontaneous beat
noise and shot noise dominate. This noise factor can be measured using optical
instrumentation. The ASE spectral density ␳ASE can be measured using an optical
spectrum analyzer. This approach to the measurement of the noise factor is
referred to below as the optical method.
The IEC defines the signal-spontaneous noise factor as the first term in Eq. Ž13.:
Fsig-sp s
2 ␳ASE
Gh␯
Ž 14 .
NOISE FIGURE OF OPTICAL AMPLIFIERS
133
FIG. 6. The optical and electrical methods of optical noise figure measurement share the same
general noise factor.
Figure 6 summarizes the development outlined above. Starting with the noise
factor definition Žsee Eq. Ž3.., the specification of noise as intensity noise or
equivalently photocurrent noise in an ideal receiver leads to the general noise
factor Žsee Eq. Ž10... This general noise factor is valid for either optical domain or
electrical domain measurements of the noise factor. At this point, the path for
optical measurements diverges from the path for electrical measurements. On the
optical measurement path Žto the left., the signal-spontaneous beat noise factor is
easily characterized by measurement of the ASE density, ␳ASE , and signal gain.
Along the optoelectronicrelectrical measurement path Žto the right., the noise
factor is measured using electrical measurements of S e and Sshot as discussed in
Section V. We note that a major advantage of the framework for noise factor
presented in this paper is the common link of the general noise factor ŽEq. Ž10..
both to optical and to optoelectronicrelectrical characterization techniques for
noise figure.
V. NOISE FACTOR OF CASCADED COMPONENTS
In this section we consider the noise factor of a cascade of optical components.
The main objective of this section is to develop an expression for the total noise
figure of a cascade of noisy components. This is an important consideration in a
range of practical applications such as telecommunications links employing cascaded amplifiers.
In an amplifier cascade, the gain increases in a multiplicative fashion while the
intensity noise increase depends on both multiplicative and additive processes,
134
BANEY, GALLION, AND TUCKER
FIG. 7. Cascade of optical amplifiers leading to an accumulation of ASE.
depending on the characteristics of the particular noise source. Each stage of
amplification adds additional noise to the signal as well as amplifying the noise
generated from previous stages. This process is illustrated in Fig. 7, which shows a
cascade of N amplifiers in which the ith stage has gain Gi and ASE spectral
density ␳ASE i . The ASE from the first amplifier is multiplied by the gain of the
second stage that in turn adds additional ASE. This process continues to the Nth
c
amplifier stage. The ASE density ␳ASE
at the output of the cascade is
c
␳ASE
s ␳ASE 1Ž G 2 G 3 . . . GN . q ␳ASE 2Ž G 3 G4 . . . GN . q ⭈⭈⭈ q␳ASE Ny 1GN q ␳ASE N .
Ž 15 .
Given the gain, G, of each amplifier stage and the ASE contribution at each stage,
the total ASE can be calculated. The signal-spontaneous noise factor Fsig-sp for the
amplifier is often used as a figure of merit indicating the amount of ASE generated
by the amplifier per unit gain. With knowledge of the gain, G, and noise factor
Fsig-sp , the total ASE density, ␳ASE can be calculated. The noise figure of a cascade
of amplifiers can then be determined in a straightforward manner as follows.
Dividing Eq. Ž15. by the total gain of the cascade, G Total s G1G 2 . . . GN , and
multiplying by the quantity Ž2rh␯ . gives the effective signal-spontaneous noise
factor of the cascade:
c
2 ␳ASE
h␯ G Total
s
2 ␳ASE 1
h␯ G1
q
2 ␳ASE 2
h ␯ G 1G 2
q ⭈⭈⭈ q
2 ␳ASE Ny 1
h␯ G1G 2 . . . GNy1
q
2 ␳ASE N
h␯ G Total
. Ž 16 .
We find from Eqs. Ž14. and Ž16. that the total signal-spontaneous noise factor
c
Fsig-sp
for a cascade of N stages of amplification is
c
Fsig-sp
s Fsig-sp, 1 q
Fsig-sp, 2
G1
q
Fsig-sp, 3
G 1G 2
q ⭈⭈⭈ q
Fsig-sp, N
G1 . . . GNy1
,
Ž 17 .
where Fsig-sp, N is the noise factor of the Nth stage. The same amplifier cascade
relation is given by Desurvire w1x and Agrawal w5x and has also been shown to be
applicable for coherent detection w23x.
If the signal-spontaneous noise factor, Fsig-sp , is measured for each amplifier in
c
the cascade, the cascade noise factor, Fsig-sp
, is calculated from Eq. Ž17. and the
expected ASE density at the end of the chain of amplifiers from Eqs. Ž16. and
NOISE FIGURE OF OPTICAL AMPLIFIERS
135
Ž17. is
c
c
␳ASE
s Fsig-sp
h␯
2
G Total .
Ž 18 .
c
This ASE density, ␳ASE
, is strictly in the same polarization as the signal light. The
total unpolarized ASE is twice the polarized ASE if the effects of polarization
hole-burning ŽPHB. or polarization-dependent loss may be neglected w3x. In large
amplifier cascades, however, PHB may become significant.
Once the cascade signal-spontaneous noise factor, Fsig-sp , is determined, shot
noise can be included according to Eq. Ž13. Žwith ␩ s 1. to compute the overall
c
signal-spontaneous and shot-noise-limited noise factor Fsig-sp,
shot of the cascade of
N stages:
c
c
Fsig-sp,
shot s Fsig-sp q
1
G1G 2 . . . GN
.
Ž 19 .
EXAMPLE: NOISE FACTOR OF THREE ELEMENT CASCADE. We now illustrate the
cascade formulas of the three-element cascade of two amplifiers and a passive
element shown in Fig. 8. The passive element may be some device such as an
optical wavelength addrdrop multiplexer or a chromatic dispersion compensator.
To determine the overall noise factor, we first determine the signal-spontaneous
c
noise factor Fsig-sp
for a cascade of three elements using Eq. Ž17.:
c
Fsig-sp
s Fsig-sp, 1 q
Fsig-sp, 2
G1
q
Fsig-sp, 3
G 1G 2
.
Ž 20 .
As shown in Fig. 8 we set G 2 to L, the transmission coefficient of the passive
element Ž L F 1.. The ASE and hence the excess noise factor contributed by the
passive element are zero, and we obtain:
c
Fsig-sp
s Fsig-sp, 1 q
0
G1
q
Fsig-sp, 3
G1 L
.
FIG. 8. Cascade of optical amplifiers and a passive element.
Ž 21 .
136
BANEY, GALLION, AND TUCKER
The noise factor including shot noise from Eq. Ž19. is:
c
Fsig-sp,
shot s Fsig-sp, 1 q
Fsig-sp, 3
G1 L
q
1
G1 L
.
Ž 22 .
From this we conclude that if G1 L is less than unity, then both the first and the
third devices must have low noise figures to minimize the overall noise figure. As
the product G1 L exceeds unity, the first amplifier dominates the overall noise
contribution. It is worth noting that with the noise figure formulations derived
here, the noise factor of a passive lossy device is equal to its loss. A 10 dB
attenuator has a noise figure of 10 dB.
Discussion
The noise figure formulation presented in Eq. Ž10. is the main result of our
theory discussion. It provides a consistent and rigorous basis for dealing with the
total noise figure where effects such as multipath interference noise are taken into
account. The formulation presented here provides a common model between
optical and electronic measurement methods allowing for measurement of the
complete noise figure.
We have also presented a reduced formulation when only signal-spontaneous
beat noise and shot noise need to be included in the model. The reduced
formulation Žsummarized in Eq. Ž13.. is useful for evaluating the effects of gain
and loss on the noise characteristics of cascades of optical components. However, it
is important to note that this reduced formulation is strictly applicable only where
signal-spontaneous beat noise and shot noise are the only noise of interest. The
reduced formulations described above are in agreement with both the IEC ŽSC86C,
Working Group 3. draft document concerning optical amplifier noise figure and
the instrumentation offered by suppliers of noise figure test equipment.
VI. MEASUREMENT OF NOISE FIGURE
Noise figure has been traditionally characterized using the so-called optical and
optoelectronic or electrical techniques w3, 12, 15᎐23x. In the optical techniques, an
optical spectrum analyzer is used to measure the amplified spontaneous emission
from which the noise factor is found using Eq. Ž13.. In the optoelectronicrelectrical method, a photodetector followed by an electrical spectrum analyzer is used to
directly measure the intensity noise from which the noise figure is determined. The
optoelectronicrelectrical method reveals the baseband frequency dependence of
the amplifier noise figure.
In both measurement methods, it is important to refer the amplifier noise
performance to a defined set of terminals. This was illustrated earlier in Fig. 5,
which shows how noise figure is measured. In Fig. 5a the input and output
reference planes are connected by a lossless waveguide Žfiber.. In Fig. 5b the
amplifier is inserted between the reference planes. Input power is defined by the
IEC as the power exiting the input connector, or cleaved fiber Žprior to the fusion
NOISE FIGURE OF OPTICAL AMPLIFIERS
137
splice connection.. To reduce the additive effects of broadband SSE power on the
input power to the EDFA, the laser sourceŽs. should be postfiltered. Polarization
randomizers are often used to reduce measurement uncertainty caused by slowly
wondering light polarization and polarization dependent elements in the test
system.
The input coupling loss can have a dramatic effect on the measured noise figure.
This is illustrated by an experience one of the authors had while participating in a
series of optical amplifier noise figure measurement seminars. A manufacturer of
optical amplifiers brought their amplifier to the HP automated noise figure
measurement system traveling with the seminar. Upon testing, the measured noise
figure was over 10 dB. The manufacturer’s amplifier experts insisted that the noise
figure was closer to 6 dB. After some investigation it was found that a dirty
amplifier input connector was the culprit. After cleaning, the amplifier performed
as expected. The effect of input coupling loss can be readily determined by using
the cascade formula Eq. Ž20. or by using Eq. Ž10.. If the input coupling loss is an
amplifier defect, then it will increase the noise figure. If, instead, it is a test system
defect, it must be corrected. For the most accurate measurements, fusion spliced
connections are preferred. At a minimum, given the impact of the input connector
losses and potential input mode mismatch, the pertinent connector details should
be recorded along with the measured noise figure data.
Optical Measurement Techniques
From Eq. Ž13., measurement of the optical noise figure requires the following
parameters to be determined:
The ASE spectral density ␳ASE in the signal polarization at the channel
wavelength
䢇
䢇
The channel wavelength
䢇
The device gain G.
The ASE spectral density is easily measured using an optical spectrum analyzer
ŽOSA.. The gain and wavelength can be measured using a variety of conventional
techniques.
The recent evolution of dense wavelength division multiplexing ŽDWDM. with
its narrow spacing of signal channels has increased the need for careful attention
to separation of the laser source spontaneous emission ŽSSE. from ASE generated
in the device under test. Laser source spontaneous emission is the amplified
spontaneous emission produced by the internal optical gain of the laser transmitter. It is very similar to the ASE produced by optical amplifiers. It is clearly
important that any nonideal source characteristics do not influence the accuracy of
the measurement. The maximum acceptable SSE to obtain a reasonable error in
the measured noise figure depends on the absolute SSE density at the amplifier
terminals. Figure 9 shows the fractional error in the measured noise factor as a
function of the SSE. We see that a source with y50 dBmrnm SSE spectral density
at the signal wavelength would add 50% to the measured noise factor. For this
138
BANEY, GALLION, AND TUCKER
FIG. 9. Noise factor error due to additive effect of source spontaneous emission ŽSSE. on noise
figure.
particular optical source, a reduction of better than 15 dB in the SSE is required
for accurate measurement. This reduction could be performed by attenuating the
test source or by using the techniques outlined below.
A number of refinements of the optical method have been developed for
accurate noise figure characterization including:
䢇
Source subtraction
䢇
Time domain extinction
䢇
Polarization extinction
䢇
Reduced source
䢇
Signal substitution.
In all these measurements, the amplifier gain is measured at the signal wavelengths
and the amplifier generated ASE is measured preferably at the same wavelength or
estimated through wavelength interpolation. Note that all the techniques described
here require accurate information regarding the effective noise bandwidth of the
OSA. The nominal measurement resolution bandwidth is not necessarily equal to
the effective optical noise bandwidth. Moreover, the effective noise bandwidth
typically varies with optical wavelength. Fortunately, manufacturers typically supply
the wavelength dependent effective noise bandwidths of their OSAs.
Source Subtraction Technique
The source subtraction technique addresses the problem of separating the SSE
from the ASE by characterizing the SSE with the EDFA bypassed w3x. As long as
the SSE spectral density is time-invariant, in principle it may be subtracted from
the total noise output of the EDFA to obtain the EDFA-generated ASE. Equation
Ž13. is modified to accommodate the subtraction yielding:
Fs
2 ␳total
Gh␯
q
1
G
y
2 ␳ SSE
h␯
.
noise factor s measured noise factor y SSE correction
Ž 23 .
NOISE FIGURE OF OPTICAL AMPLIFIERS
139
In Eq. Ž23., ␳total is the total ASE density from the optical amplifier including the
amplified source spontaneous emission, both in the same polarization state as the
signal. In practice, the ASE is usually assumed to be unpolarized and the densities
2 ␳total and 2 ␳ SSE are replaced by their corresponding unpolarized densities. Since
the presence of the signal masks the measurement of the noise densities at the
signal wavelength, measurements adjacent to the signal are used to interpolate the
noise at the signal wavelength as shown in Fig. 10. In the figure, the input signal
spectrum clearly shows significant SSE.
This technique is applicable to multichannel characterization of EDFAs under
certain restrictions. It requires an OSA with sufficient selectivity to measure
between closely spaced DDM channels. The effect of cumulative SSE needs to be
considered. In particular, if the DWDM test lasers are combined using broadband
fused couplers, the broadband SSE from all channels will be additive at each
measurement wavelength. This can result in the subtraction of two noise measurements of similar magnitude, thus increasing the error in the correction. Limiting
the total amplified SSE density to be less than or equal to the ASE density
generated by an ideal amplifier with a 3 dB noise figure, we find that the composite
SSE power would preferably be less than 2 h␯ Bo . At a wavelength of 1.55 ␮ m, this
corresponds to a maximum composite SSE density of ;y45 dBmrnm at the
EDFA input terminals.
FIG. 10. Optical spectra for source subtraction method of noise figure measurement: Ža. incident
signal and SSE, Žb. output spectrum.
140
BANEY, GALLION, AND TUCKER
Time Domain Extinction Technique
The time domain extinction ŽTDE. method takes advantage of the slow gain
dynamics of the EDFA to reduce the effect of SSE on the noise figure measurement w3, 18, 19, 24x. When the EDFA is driven into saturation, the gain and the
ASE depend on the average incident signal intensity. When the signal is pulsed-off,
the EDFA gain recovers to a new steady state level. The recovery time is slow
enough Žmicrosecond time-scales . such that the ASE from the amplifier may be
measured before it changes appreciably. Since the signal and SSE are no longer
present, the measured ASE corresponds to the actual ASE generated by the optical
amplifier. The signal is then pulsed back on and the process repeats.
A measurement setup for this technique is shown in Fig. 11. When the input
switch is closed as shown in Fig. 11a, the amplifier is illuminated by signal and
noise. In Fig. 11b, the input switch is opened extinguishing the signal and the
output switch closes. This enables the OSA to sample the ASE produced by the
amplifier. When the gating rate is slow compared to the gain recovery time of
the amplifier, the response is as shown in Fig. 12a. Energy storage in the amplifier
causes a signal transient as the signal is gated into the amplifier operating in the
small signal regime w1, 3x. The flat portion of the waveform following the transient
is the steady state condition. If the ASE is measured soon after the signal is gated
off, it will be the same ASE generated in the presence of signals. When the gating
rate is faster than the gain recovery time of the amplifier, the response is as shown
in Fig. 12b. In this case the effective input power that determines the amplifier
saturation state is the time average of the gated signal. The ASE waveform is
triangular with an offset during the signal-on interval due to the additive effect of
the SSE. If the ASE is sampled halfway through the positive going slope as shown,
the ASE will correspond to the ASE generated by the amplifier in the presence of
the average signal power. The error due to gain recovery varies linearly with pump
power w3x. For EDFAs, pulse repetition rates of 25 kHz or more are typically used.
FIG. 11. Time-domain extinction method for amplifier ASE measurement. Ža. Signal is setting
amplifier saturation state. Žb. Signal disconnected, OSA measures ASE.
NOISE FIGURE OF OPTICAL AMPLIFIERS
141
FIG. 12. Signal and ASE diagrams for domain extinction method for amplifier. Ža. Low frequency
regime. Žb. High frequency regime.
The presence of active feedback and control circuits will also affect the choice of
the signal gate-rate.
The extinction ratio of the switches shown in Fig. 11 is important. Multiple
switch stages may be required to obtain complete suppression of the signal. When
the depth of the extinction is not sufficient to completely reject the signal,
interpolation is used to estimate the ASE at the signal wavelength.
With the addition of a small signal probe, a swept-wavelength characterization of
the EDFA gain spectrum can be performed w3, 25x. This permits gain tilt characterization for DWDM applications by measuring the variation in gain between the
test laser wavelengths. Figure 13 shows a typical measurement of gain and noise
figure using this technique. In Fig. 13a, the pulsed edge-emitting LED ŽEELED.
probe provides a broadband stimulus from a wavelength of 1525 to 1575 nm. Three
measurements are performed during the time interval when the saturating source
is gated off:
1. Calibration: small-signal probe power versus wavelength with EDFA bypassed: Pcal Ž ␭.
2. Small-signal probe power and ASE power versus wavelength with EDFA
inserted: P1Ž ␭.
3. ASE power versus wavelength with EDFA inserted Žprobe not sampled.:
Ž
.
P2 ␭
The amplifier gain is calculated using:
G Ž ␭. s
P1 Ž ␭ . y P2 Ž ␭ .
Pcal Ž ␭ .
.
Ž 24 .
Figure 13b shows a measured noise figure using this technique. The noise factor
was calculated using Eq. Ž13. with ␳A S E Ž ␭. s P2 Ž ␭.rŽ2 Bo ., where Bo is the
effective noise bandwidth of the OSA.
142
BANEY, GALLION, AND TUCKER
FIG. 13. Ža. Dynamic gain and noise figure measurement setup. Žb. Measurement with a saturation
wavelength of 1550 nm.
Polarization Extinction Technique
The polarization extinction technique provides another way to deal with the
problem of excess source noise w3, 18x. In this method, a fixed, or known,
relationship is assumed to exist between the magnitude of the ASE generated by
the optical amplifier in orthogonal polarizations. Therefore, if the ASE is measured in one polarization, the ASE in the signal polarization is determined. In the
measurement setup shown in Fig. 14, a polarized signal source is directed to the
optical amplifier. To measure the ASE, the polarization controller following
the amplifier is set such that the signal polarization is orthogonal to the preferred
transmission axis of the polarizer. Under these conditions, the signal, the amplified
SSE, and one-half the ASE are reflected away. The OSA measures only the ASE
orthogonal to the signal. Noise factor is calculated from Eq. Ž13. where the ASE
densities are assumed equal in each polarization.
FIG. 14. Polarization extinction method for amplifier noise figure measurement. Laser has polarized output. OBPF, optical bandpass filter; PC, polarization controller; Pol, polarizing beam splitter;
OSA, optical spectrum analyzer.
NOISE FIGURE OF OPTICAL AMPLIFIERS
143
In practice, the rejection of the signal may not always be complete. The signal
may still contribute to the displayed spectrum. Even so it will be adequate to
sufficiently reduce the noise figure error. As with the TDE technique, when the
depth of the null is not sufficient as determined from Fig. 9, interpolation is used
to estimate the ASE at the signal wavelength.
Factors limiting the SSE rejection include:
The time required to adjust the polarization controller to obtain the desired
null depth
䢇
䢇
Polarization mode dispersion
䢇
The stability of test system birefringence Žtest cable stability .
䢇
The quality of polarizer rejection
䢇
SSE from other DWDM channels
The amplifier gain is measured by bypassing the polarizer and performing the gain
measurement in the conventional manner. Beyond the necessary rejection of the
signal ASE, there is an added benefit with this technique of allowing measurement
closer to the signal wavelength. The limited wavelength selectivity of an OSA
means that the ability to measure low levels of ASE decreases as the OSA is tuned
close to the strong test channel. The 25 dB, or more, rejection of the signal that
this technique provides allows for a close-in measurement of the ASE around
the optical signal. An example of a rejected signal Žamplifier bypassed. and the
case where the polarization controller is set to maximize the signal is shown in
Fig. 15 w3x.
Signal-Substitution Technique
The signal-substitution technique allows for measurement of the ASE at the
channel wavelength by removing the signal and adding power to adjacent channels
w26x. This technique reduces the wavelength selectivity requirement on the OSA for
a given channel spacing. This allows for measurement on dense DWDM channel
plans. The method is based on the locally homogeneous nature of the optical
amplifier gain spectrum. The concept is illustrated in Fig. 16. The signal power at
FIG. 15. Input signal and laser spontaneous emission rejection using polarization extinction.
144
BANEY, GALLION, AND TUCKER
FIG. 16. Illustration of the signal substitution technique: Ža. input DWDM channels, Žb. signal at
test channel is displaced to adjacent channels.
the channel wavelength to be characterized is removed. The removed signal power
that had contributed to the local and global amplifier saturation state is accounted
for by increasing the power of the adjacent channels. For closely spaced channels,
⌬ P, the required increase in adjacent channel powers is given by
⌬ Piy1 , ⌬ Piq1 s
Pi Gi
Giy1 q Giq1
,
Ž 25 .
where Pi and Gi are the power and gain of the test channel, respectively. The noise
figure measurements are performed in combination with the source subtraction
method to reduce the impact of the source spontaneous emission. Since the
method provides constant input power to the EDFA during the measurement, it
does not interact with optical power control feedback circuits employed with most
EDFAs.
DWDM Characterization: Reduced Channel Technique
In dense WDM application with a large number of input channels, the cost of
assembling and maintaining a large number of stable test-quality sources provides
motivation to reduce the required DWDM laser array. In these applications the
NOISE FIGURE OF OPTICAL AMPLIFIERS
145
FIG. 17. Illustration of the amplifier spectrums for the reduced-source technique. Ža. DWDM
channel plan. Žb. Equivalent reduced-source representation. SHB, spectral hole-burning.
reduced-channel technique may be applied w27x. The underlying premise is that the
EDFA behaves like a homogeneously broadened amplifier across a limited wavelength range. The EDFA, across its entire gain band, has significant homogeneous
broadening. That is, all the signals across the EDFA gain band can equally access
the stored energy responsible for gain anywhere across the band. However,
measurements have revealed the presence of spectral hole-burning ŽSHB. with a
dependency of ;0.3 dB for each dB of gain compression w1, 3, 29x. Thus the
accuracy of a method that uses a single high-power channel to represent the
ensemble of DWDM channels would be limited by SHB. In general, in the
presence of SHB, N channels are used to represent M actual channels Ž N F M .
across the wavelength range of the channel plan. The separation of the N channels
is determined by the widths of the spectral holes. For example, a minimum of one
channel per SHB hole-width should be used. Spectral hole widths vary from about
3 nm to greater than 10 nm across the EDFA gain region. The narrower holes tend
to be around the 1530 nm region which implies more saturating channels to cover
this region. The reduced-source concept is shown in Fig. 17. In Fig. 17a, the actual
test channel plan is illustrated along with the SHB holewidth. A possible set of
representative channels is indicated in Fig. 17b.
In physical terms, the representative powers applied to the amplifier must ensure
that the amplifier state, as set by the relative levels of the metastable-state and
ground-state populations, is the same for the complete channel and the reduced
channel technique. The representative power, Prep for a set of q wavelengths is
146
BANEY, GALLION, AND TUCKER
equal to w27x:
Prep s
1
␭rep Grep
Ý Pq ␭ q Gq .
Ž 26 .
q
This is another way of saying that the reduced channel representation across a
given homogeneously broadened portion of the gain spectrum must generate the
same corresponding photon flux as that generated by the full complement of
channels across the same portion of the gain spectrum. In this technique, the
various channel gains are not known in advance, so they can be set equal to Grep as
a starting guess. Measurements using this technique have shown rapid convergence, typically in about two iterations w27x.
Optoelectronic / Electrical Measurement Techniques
The most complete evaluation of noise in an amplifier or other optical component is performed using a photodetector and an electrical spectrum analyzer ŽESA.
to examine the intensity noise generated by the optical amplifier w3, 9, 12, 15, 22,
28x. The optoelectronicrelectrical measurement method has a major advantage
over optical methods. Unlike optical methods, all amplifier-generated intensity
noise that would occur in an actual receiver such as multipath interference noise,
double Rayleigh scattering, and pump-induced noise are measured by this technique. Optoelectronic methods therefore provide the only means to completely
characterize the intensity noise generated by an optical amplifier.
A measurement setup for the optoelectronic technique is shown in Fig. 18.
Optical filters following the source and preceding the detection are shown to
indicate that the source linewidth and receiver optical bandwidth are test parameters that must be specified. This is due to the optical bandwidth dependence of
various noise processes such as interference noise and spontaneous-spontaneous
beat noise.
The general noise factor relation ŽEq. Ž10.. applicable to both optical and
optoelectronic methods provides the starting basis for the optoelectronic method.
FIG. 18. Noise figure measurement using an electrical spectrum analyzer ŽESA.. OBPF, optical
bandpass filter; ATT, optical attenuator.
147
NOISE FIGURE OF OPTICAL AMPLIFIERS
For an ideal receiver, with ␩ s 1, the total noise factor is as given in Eq. Ž10.,
repeated here for convenience,
Ftotal Ž ␯ , f . s
Se Ž ␯ , f .
2 h␯ G Pin
2
q
Sshot
2 h␯ G 2 Pin
,
Ftotal s Fexcess q Fshot
Ž 27 .
where S e Ž ␯ , f . is the amplifier-generated excess intensity noise and Sshot is the
shot noise due to the total average power exiting the amplifier. The dependence of
the noise figure on baseband frequency f is of particular importance with optoelectronic techniques. There are several approaches to making this measurement as
discussed in w12, 15, 17, 22x. More detail on the discussion given here may also be
found in w3x.
The net noise power density displayed on the ESA with the setup shown in Fig.
18 consists of contributions from the excess amplifier noise, S e Ž f .< ED FA , the
amplified excess source noise, S e Ž f .< source , the shot noise, Si < shot , and the thermal
noise, S ESAŽ f .< th :
S ESA Ž f . < mea s k Ž f .
2
ᑬ 2 Se Ž f .
q S ESA Ž f .
th
EDFA
q ᑬ 2 G 2S e Ž f .
source
q Si < shot
w WrHzx .
Ž 28 .
< k Ž f . 2 < is nominally 50 ⍀, but it must be calibrated across the measurement
frequency range. Electrical preamplifier limitations, impedance mismatches, and
the frequency response of the ESA and photodetector will cause < k Ž f . 2 < to vary
with baseband frequency. ᑬ is the DC responsivity of the photodetector with units
of wArWx. G is the gain of the optical amplifier. In the following, we assume that
the amplifier gain and the optoelectronic detection calibration has been determined using standard methods as described in w3x. The test method must extract
the excess intensity noise S e Ž f .< ED FA generated by the EDFA from the measurement system characteristic and the source and receiver excess noises. Once this is
performed the noise factor can be calculated using Eq. Ž27..
Source Noise Subtraction Technique:
With this method a first measurement is made with the EDFA bypassed to
determine the level of excess noise from the source. The first ESA measurement
yields:
S ESA Ž f .
mea . 噛1
s kŽ f .
2
ᑬ 2 Se Ž f .
source
q 2 qᑬ ² Pin : q S ESA Ž f .
th .
Ž 29 .
< k Ž f . 2 < and ᑬ are known from the system calibration, the input power, Pin , is
measured using an optical power meter, and the thermal noise is determined by
blocking the input light and recording the ESA displayed noise. Thus the excess
source noise S e Ž f .< source is characterized.
148
BANEY, GALLION, AND TUCKER
Next the EDFA is inserted and a second measurement is made with the
calibrated attenuation, ␣ , set such that the receiver does not saturate:
S ESA Ž f .
mea . 噛 2
s kŽ f .
2
ᑬ 2␣ 2 S e Ž f .
q S ESA Ž f .
ED FA
q ᑬ 2␣ 2 G 2 S e Ž f .
source
q 2 qᑬ ␣ ² Pave :
th .
Ž 30 .
The average incident power ² Pave : including both amplified signal and ASE is
measured with an optical power meter. This results in one equation and one
unknown Žthe amplifier excess noise. with the solution:
Se Ž f .
ED FA
s
S ESA Ž f .
mea . 噛 2
y S ESA Ž f .
2
kŽ f . ᑬ ␣
2
th
2
y
2 q² Pave :
ᑬ␣
y G 2 S e Ž f . . Ž 31 .
Amplifier noise s Ž ESA noise y thermal noise . recei¨ er correction
y shot noise y amplified source excess noise
With the excess amplifier noise known, the noise figure is calculated according
to Eq. Ž27..
Constant Power Technique
With this method, a first measurement is made with the EDFA bypassed and the
input attenuator is set for unity transmission Že.g., ␣ s 1. w15x. A spectral measurement with the ESA yields:
S ESA Ž f .
mea . 噛1
s kŽ f .
2
ᑬ 2 Se Ž f .
source
q 2 qᑬ ² Pin : q S ESA Ž f .
th .
Ž 32 .
The amplifier is inserted and the attenuation is increased Ž ␣ - 1. such that the
average power is the same as in the first measurement. If the amplified signal and
ASE are the only powers present at the detection, the attenuation would equal
␣s
² Pin :
Ž 33 .
² GPin : q ² PASE :
and the displayed spectrum is
S ESA Ž f .
mea . 噛 2
s kŽ f .
2
ᑬ 2␣ 2 S e Ž f .
EDFA
q ᑬ 2␣ 2 G 2 S e Ž f .
q2 qᑬ ␣ ² GPin : q ² PASE :
source
q S ESA Ž f .
th
Ž 34 .
with the constraint that the signal and ASE satisfy
² GPin : 4 ² PASE : .
Ž 35 .
NOISE FIGURE OF OPTICAL AMPLIFIERS
149
Then subtracting Eq. Ž32. from Eq. Ž34. yields:
S ESA Ž f .
2
mea . 噛 2
s k Ž f . ᑬ 2␣ 2 S e Ž f .
EDFA .
Ž 36 .
S e Ž f .< ED FA is then determined by using the measured receiver transfer function.
In practice, it is advisable to use a low-noise optical receiver with a high
saturation power preceding the electrical spectrum analyzer. This is particularly
important where high channel powers require optical attenuation preceding the
receiver to limit saturation. Optical attenuation reduces the detected intensity
noise relative to the thermal and shot noise making it desirable to use a receiver
which can sustain high optical power levels.
Impact of Source Linewidth and Recei¨ er Bandwidth
In a system otherwise free of optical reflections, internal reflections within the
optical amplifier convert signal phase and frequency noise into intensity noise w3, 8,
9, 11x. The amount of intensity noise depends equally on the strength of the
reflections and on the laser linewidth. Thus the signal linewidth becomes a
stimulus parameter, much like optical power or signal wavelength. It can be argued
that an ideal amplifier has no MPI and thus the conversion of phase noise to
intensity noise through amplifier MPI is an amplifier nonideality which should be
included in the amplifier noise figure. Certainly, this increase in intensity noise
manifests itself as increased bit-error rates at the destination communications
receiver. Therefore, the source phase noise, or, in practical terms, its linewidth,
should be noted as a source parameter. The receiver bandwidth, Bo , also determines the contribution spontaneous-spontaneous beat noise will make to the noise
figure as suggested in Fig. 3. This bandwidth may be set by the filter shape of a
DWDM demultiplexer or by the net lineshape of the atomic transitions responsible
for the amplifier gain. In any case, this should be specified when spontaneousspontaneous beat noise is expected to contribute to the noise figure.
Example RIN Transfer Technique of Optoelectronic Noise Figure Measurement
The noise figure of a 980 nm copropagating amplifier with integrated tap unit
was measured using the optoelectronic method with the RIN transfer noise
calibration method. The amplifier gain was measured to be 35. First, the opto-electronic receiver was calibrated using the RIN transfer technique w3x. A dielectric
thin film filter of approximately 433 GHz FWHM was placed after an EDFA to
provide a calibration noise source. The spectrum, SE Ž ␯ ., of the noise source was
measured with an OSA. The expected RIN for the ASE source was calculated
according to w3x,
RINcal Ž f . s
FT
FTy1 SE Ž ␯ . 4
2
HS
E
Ž ␯ . d␯
2
,
Ž 37 .
150
BANEY, GALLION, AND TUCKER
FIG. 19. Data from electrical-method noise figure measurement showing calibration, amplifier
total, and receiver noise traces. Dependence of EDFA noise figure on baseband frequency is shown in
the middle trace.
which yielded a RIN of y117.3 dBrHz for the calibration source. This source was
then measured using a photodetector electrical spectrum analyzer combination as
shown by the top trace in Fig. 19. The average power of the ASE source was 1.342
mW. With this information and the following definition of RIN,
RINcal Ž f . s
Se Ž f .
P2
,
Ž 38 .
the absolue magnitude of the electrical spectrum analyzer display was calibrated
with units of WrHz plotted on a logarithmic scale.
Next, the thermal noise was measured with the input light to the receiver
blocked as shown by the lower trace in Fig. 19. In the next step, the DUT EDFA
was connected and illuminated with a semiconductor DFB laser with y18.2 dBm
of shot-noise-limited output at a wavelength of 1558.8 nm. The corresponding noise
trace is shown in Fig. 19. Note that at frequencies below 500 MHz there is an
increase in the EDFA noise. This is due to optical reflections internal to the
amplifier causing an MPI-induced noise increase. Using Eq. Ž28., the noise figure
at 300 MHz was 7.8 dB, rising to about 16 dB at low frequencies. Near 1 GHz, the
noise figure dropped by approximately 2 dB. This is in contrast to a noise figure of
5.8 dB as measured using the optical method and Eq. Ž13.. The difference is due to
amplifier-generated intensity noise that the opto-electronic method measures which
is neglected with the optical test methods.
At a risk of over-generalizing, and adding the cautionary note that the basic
techniques discussed below will evolved over time, we summarize below the merits
and disadvantages of the various optical and optoelectronicrelectrical measurement methods.
NOISE FIGURE OF OPTICAL AMPLIFIERS
151
Optical Methods
Time domain extinction. Merits: Provides rapid measurement. Can be used in
conjunction with small-signal probe to measure dynamic gain. Works well with the
reduced-source technique. Allows possibility for noise measurement at the signal
wavelength. Disadvantages: Insertion loss of gating switches, more complicated
measurement setup.
Source subtraction. Merits: Simple to implement. Disadvantages: sensitive to
additive SSE from DWDM channels, requires stable SSE.
Polarization extinction. Merits: Allows possibility for noise measurement at the
signal wavelength. Disadvantages: longer measurement time, sensitive to polarization mode dispersion, polarization stability and polarization hole-burning.
Signal substitution. Merits: Reduces wavelength resolution requirement of the
OSA, maintains constant power to the EDFA, simple to implement. Disadvantages:
sensitive to spectral hole-burning in certain applications.
Reduced-source. Merits: Reduces size of DWDM test laser array. Disadvantages: iterative method Ž;2 iterations ., largest benefit obtained where the SHB
widths are wider than DWDM channel separations.
Optoelectronicr Electrical Methods:
RIN transfer technique. Merits: Provides complete noise figure with baseband
frequency dependence of noise factor. Measures all intensity noise generated by
the EDFA. Disadvantages: If shot-noise-limited source is not available, source
output noise must be stable to permit subtraction.
Constant power. Merits: Provides complete noise figure with baseband frequency dependence of noise factor. Measures all intensity noise generated by the
EDFA. Disadvantages: If shot-noise-limited source is not available, source output
noise must be stable to permit subtraction. Also requires ASE to be small
compared to amplified signal.
The ultimate decision on the measurement method will depend on the design
and application of the amplifier. Among the optical measurement techniques, the
authors have found that the TDE approach combined with a small signal probe
and the reduced source technique represents a powerful solution for amplifier
characterization. When a measurement of the complete noise figure is required,
the optoelectronic methods are employed using the RIN transfer calibration
technique.
VII. EDFA TEST SYSTEMS
This paper thus far has focused mainly on the theoretical and measurement
methods. The amplifier measurement implementation requires the assembly and
coordination of a number of optical and electrical instruments. The response times
of each instrument must be carefully synchronized with the rest of the equipment
152
BANEY, GALLION, AND TUCKER
FIG. 20. Photograph of an EDFA test system showing optical instrumentation and computer
control and display.
to reduce test time and measurement uncertainty. Often there is a significant
amount of software involved to implement the measurement algorithms. An
example of an EDFA test system is shown in Fig. 20. In the test rack are lasers for
stimulus, optical power meters, an optical spectrum analyzer, and a test set for
optical signal processing and supplying and receiving signals from the amplifier
under test. A computer is used to control the measurement equipment and process
the measured data. Often the measurements are performed over temperature
where the amplifier is placed in a temperature-controlled enclosure. When fusionspliced connections are used, highest measurement accuracy is obtained. A number
of the measurement uncertainties are determined by instrumentation limitations
such as the polarization dependence of the measurement equipment. Sometimes
polarization scrambling is used to reduce this uncertainty. While commercial
amplifier test systems offer the convenience a packaged rack-mounted measurement solution, their main contribution lies in the implementation of the measurement algorithms within the context of instrument limitations.
VIII. SUMMARY
A number of different noise mechanisms originating from optical gain, loss, and
interference contribute to the total noise figure. A general noise figure formula has
NOISE FIGURE OF OPTICAL AMPLIFIERS
153
been derived and shown to be consistent with the optical domain and the optoelectronicrelectrical domain. The standard signal-spontaneous beat noise factor formula is a direct simplification of the more general relation. The general noise
figure formulation requires no assumptions on the types of noise generated by the
amplifier.
We have surveyed a number of different measurement techniques. Noise figure
can be characterized using either an optical spectrum analyzer or a photodetector
followed by an electrical spectrum analyzer. Both methods are based on the same
fundamental noise figure definition. Optical methods provide a simple but incomplete characterization of the noise produced by an optical amplifier. However,
optical methods do provide an accurate means of obtaining Fsig-sp that is useful for
cascade calculations of noise figure. Optoelectronicrelectrical methods yield complete information on the noise figure but have fewer options for dealing with
source excess noise that could easily be mistaken for amplifier-generated noise.
Because the optoelectronicrelectrical and optical methods are based on the same
original noise figure equation, given by Eq. Ž10., their results compared well in the
example at higher baseband frequencies where the effect of the multipath interference is reduced.
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